I see nothing wrong with using a nurse "tool belt".

I like the Nurse Pro Pack bags. I initially started out with their EMT pack because it was smaller and kept everything more contained because the flap velcros shut. Once I moved to the ER, I needed something larger and now I use their Nurse Pack which is roomier and it's easier to get to the supplies I need when I'm pressed for time. It's not really that noticable since I leave my scrub shirt untucked. It's a little heavy but I would be lost without it and I'm much more efficient having it. Sure, lots of supplies are in the patient rooms but it never fails when I need something, the stock has ran dry and I waste too much time hunting down what I need. Plus, I can't stand to have my pockets bulging out. That looks much nerdier than my tool belt in my opinion. Good luck with whatever you decide.